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Keywords = voice coil actuator

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17 pages, 7150 KB  
Article
Dual Halbach Array Compact Linear Actuator with Thrust Characteristics Part I Simulation Result
by Jumpei Kuroda, Ryutaro Ono, Takumu Takayama, Shinobu Kasamatsu, Ikkei Kobayashi, Daigo Uchino, Kazuki Ogawa, Taro Kato, Keigo Ikeda, Ayato Endo, Hideaki Kato and Takayoshi Narita
Actuators 2025, 14(10), 476; https://doi.org/10.3390/act14100476 - 28 Sep 2025
Viewed by 865
Abstract
The application of mechanical products in many situations involves linear motion. The cylinder head of an internal combustion engine (ICE), a mechanical product, contains intake and exhaust valves. These valves open or close using the linear motion converted by the camshafts rotated by [...] Read more.
The application of mechanical products in many situations involves linear motion. The cylinder head of an internal combustion engine (ICE), a mechanical product, contains intake and exhaust valves. These valves open or close using the linear motion converted by the camshafts rotated by the engine. A typical engine is operated with a single cam profile; depending on the engine rotation, there are areas where the cam profiles do not match, resulting in a poor engine performance. An intake and exhaust system with an actuator can solve this problem. In a previous study on this system, the geometry and processing during manufacturing were complex. Therefore, in response, a linear actuator operated by Lorentz force with a coil as the mover was designed in this study. Through an electromagnetic field analysis using the finite element method, a three-phase alternating current was applied to the coil, assuming that it would be used as a power source for a general inverter. Consequently, the thrust obtained in the valve-actuation direction was 56.7 N, indicating improved axial thrust over the conventional model. Full article
(This article belongs to the Section High Torque/Power Density Actuators)
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17 pages, 8499 KB  
Article
Integrated Design and Experiment of a Micro-Vibration Isolation and Pointing Platform for Large Space Optical Payloads Based on Voice Coil Motors
by Yilin Guo, Jian Zhou, Zehao Gao, Bo Feng and Minglong Xu
Sensors 2025, 25(4), 1179; https://doi.org/10.3390/s25041179 - 14 Feb 2025
Cited by 5 | Viewed by 1986
Abstract
This paper presents the design of an integrated micro-vibration isolation and pointing platform with a four-leg structure, incorporating pitch and yaw adjustment functions using voice coil motors. The primary objective is to mitigate the impact of spacecraft-generated micro-vibrations on the pointing accuracy and [...] Read more.
This paper presents the design of an integrated micro-vibration isolation and pointing platform with a four-leg structure, incorporating pitch and yaw adjustment functions using voice coil motors. The primary objective is to mitigate the impact of spacecraft-generated micro-vibrations on the pointing accuracy and imaging clarity of large space optical payloads while adhering to lightweight requirements. The research methodology encompasses three main phases. Initially, a simplified dynamic model of the integrated platform is established, and dynamic control equations are derived based on the proportional–integral–derivative (PID) control strategy. The effects of centroid deviation and control parameters on the control efficacy are analyzed. Subsequently, a principle prototype of the two-dimensional micro-vibration isolation and pointing platform is designed, detailing the development of the membrane, actuator, legs, and integrated system. Finally, a ground test verification system is implemented under gravity unloading conditions using elastic strings. The experimental results demonstrate the platform’s effective vibration isolation and pointing capabilities, achieving a 23 dB attenuation effect at the fundamental frequency. Furthermore, the PID control algorithm exhibits enhanced isolation performance at low frequencies and facilitates directional tracking of target signals. Full article
(This article belongs to the Special Issue Spacecraft Vibration Suppression and Measurement Sensor Technology)
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16 pages, 8423 KB  
Article
Development of Spherical Actuator with L-Shaped Yoke
by Yu-Wen Huang, Hao-Wen Chung, Yu-Ming Chen, Chien-Sheng Liu and Ming-Fu Chen
Actuators 2025, 14(1), 30; https://doi.org/10.3390/act14010030 - 15 Jan 2025
Cited by 1 | Viewed by 2109
Abstract
In this paper, a two-DOF L-shaped yoke spherical actuator based on the principle of traditional voice coil actuators is developed. By utilizing the shape characteristics of the yoke and the magnetization direction of the magnet, the magnetic flux is concentrated and the magnet [...] Read more.
In this paper, a two-DOF L-shaped yoke spherical actuator based on the principle of traditional voice coil actuators is developed. By utilizing the shape characteristics of the yoke and the magnetization direction of the magnet, the magnetic flux is concentrated and the magnet is shared, thereby improving the performance of the actuator. In the design process, SOLIDWORKS 2018 software is used for design modeling and assembly simulation, ANSYS Maxwell 2018 software is employed for magnetic circuit analysis and electromagnetic simulation, while MATLAB is utilized for analyzing the dynamic characteristics through a mathematical model. A prototype was also fabricated, and torque measurement experiments were conducted to verify the performance and feasibility of the proposed design. Full article
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16 pages, 25584 KB  
Article
Hand Teleoperation with Combined Kinaesthetic and Tactile Feedback: A Full Upper Limb Exoskeleton Interface Enhanced by Tactile Linear Actuators
by Daniele Leonardis, Massimiliano Gabardi, Simone Marcheschi, Michele Barsotti, Francesco Porcini, Domenico Chiaradia and Antonio Frisoli
Robotics 2024, 13(8), 119; https://doi.org/10.3390/robotics13080119 - 7 Aug 2024
Cited by 4 | Viewed by 6222
Abstract
Manipulation involves both fine tactile feedback, with dynamic transients perceived by fingerpad mechanoreceptors, and kinaesthetic force feedback, involving the whole hand musculoskeletal structure. In teleoperation experiments, these fundamental aspects are usually divided between different setups at the operator side: those making use of [...] Read more.
Manipulation involves both fine tactile feedback, with dynamic transients perceived by fingerpad mechanoreceptors, and kinaesthetic force feedback, involving the whole hand musculoskeletal structure. In teleoperation experiments, these fundamental aspects are usually divided between different setups at the operator side: those making use of lightweight gloves and optical tracking systems, oriented toward tactile-only feedback, and those implementing exoskeletons or grounded manipulators as haptic devices delivering kinaesthetic force feedback. At the level of hand interfaces, exoskeletons providing kinaesthetic force feedback undergo a trade-off between maximum rendered forces and bandpass of the embedded actuators, making these systems unable to properly render tactile feedback. To overcome these limitations, here, we investigate a full upper limb exoskeleton, covering all the upper limb body segments from shoulder to finger phalanxes, coupled with linear voice coil actuators at the fingertips. These are developed to render wide-bandwidth tactile feedback together with the kinaesthetic force feedback provided by the hand exoskeleton. We investigate the system in a pick-and-place teleoperation task, under two different feedback conditions (visual-only and visuo-haptic). The performance based on measured interaction forces and the number of correct trials are evaluated and compared. The study demonstrates the overall feasibility and effectiveness of a complex full upper limb exoskeleton (seven limb-actuated DoFs plus five hand DoFs) capable of combined kinaesthetic and tactile haptic feedback. Quantitative results show significant performance improvements when haptic feedback is provided, in particular for the mean and peak exerted forces, and for the correct rate of the pick-and-place task. Full article
(This article belongs to the Section Neurorobotics)
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14 pages, 6550 KB  
Article
Research on Active Repetitive Control for Tracking Lissajous Scan Trajectories with Voice Coil Motors Actuated Fast Steering Mirror
by Lin Wang, Shijiao Liu, Shuning Liang, Xuelian Liu and Chunyang Wang
Fractal Fract. 2024, 8(3), 128; https://doi.org/10.3390/fractalfract8030128 - 22 Feb 2024
Cited by 2 | Viewed by 2598
Abstract
The performance of laser beams in tracking Lissajous scan trajectories is severely limited by beam jitter. To enhance the performance of fast steering mirror (FSM) control in tracking Lissajous scan trajectories, this paper proposed a fractional order active disturbance rejection controller (FOADRC) and [...] Read more.
The performance of laser beams in tracking Lissajous scan trajectories is severely limited by beam jitter. To enhance the performance of fast steering mirror (FSM) control in tracking Lissajous scan trajectories, this paper proposed a fractional order active disturbance rejection controller (FOADRC) and verified its effectiveness in improving system scanning tracking accuracy. A dynamic mathematical model of a fast steering mirror was studied, and the design of parameters for the control mode of the closed-loop system was determined. A reduced-order linear active disturbance rejection controller suitable for FSM systems was designed, and the corresponding fractional-order proportional differentiation (FOPD) controller was determined according to the mathematical model. The use of the designed controller enabled high-performance tracking of high-frequency Lissajous scanning curves (X-axis 500 Hz, Y-axis 350 Hz) and met the need for high-frequency repetitive scanning. The controller has the characteristics of simple implementation and low computational complexity and is suitable for closed-loop control applications in engineering. Full article
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24 pages, 3091 KB  
Review
A Review of Mechanical Fine-Pointing Actuators for Free-Space Optical Communication
by Martynas Milaševičius and Laurynas Mačiulis
Aerospace 2024, 11(1), 5; https://doi.org/10.3390/aerospace11010005 - 20 Dec 2023
Cited by 34 | Viewed by 8769
Abstract
This paper presents a state-of-the-art overview of fine beam steering mechanisms for free-space optical communication on satellites. Precise beam pointing is a critical task for the successful operation of free-space optical communication systems. Based on past research and ongoing projects, the use of [...] Read more.
This paper presents a state-of-the-art overview of fine beam steering mechanisms for free-space optical communication on satellites. Precise beam pointing is a critical task for the successful operation of free-space optical communication systems. Based on past research and ongoing projects, the use of fast steering mirrors (FSMs) is still the most popular solution for free-space optical communication applications. Although a variety of commercial off-the-shelf (COTS) FSM solutions exist, there is limited publicly available data on these solutions in the space environment. Three main actuation principles are considered (electro-static force actuated, magnetic force actuated, piezo-effect actuated) and reviewed using available data from past space missions. The article describes the most important criteria in the choice of a fine beam steering solution for free-space optical communication in space. Full article
(This article belongs to the Special Issue Advanced Spacecraft/Satellite Technologies)
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13 pages, 4555 KB  
Article
Discrimination Accuracy of Sequential Versus Simultaneous Vibrotactile Stimulation on the Forearm
by Nashmin Yeganeh, Ivan Makarov, Árni Kristjánsson and Runar Unnthorsson
Appl. Sci. 2024, 14(1), 43; https://doi.org/10.3390/app14010043 - 20 Dec 2023
Cited by 5 | Viewed by 2994
Abstract
We examined discrimination accuracy of vibrotactile patterns on the upper forearm using a 2 × 3 array of voice coil actuators to generate 100 Hz vibrotactile stimulation. We evaluated participants’ ability to recognize distinct vibrotactile patterns presented both simultaneously (1000 ms) and sequentially [...] Read more.
We examined discrimination accuracy of vibrotactile patterns on the upper forearm using a 2 × 3 array of voice coil actuators to generate 100 Hz vibrotactile stimulation. We evaluated participants’ ability to recognize distinct vibrotactile patterns presented both simultaneously (1000 ms) and sequentially (500 ms with a 450 ms interval). Recognition accuracy was significantly higher for sequential (93.24%) than for simultaneous presentation (26.15%). Patterns using 2–3 actuators were recognized more accurately than those using 4–5 actuators. During sequential presentation, there were primacy and recency effects; accuracy was higher for the initial and final stimulations in a sequence. Over time, participants also demonstrated a learning effect, becoming more adept at recognizing and interpreting vibrotactile patterns. This underscores the potential for skill development and emphasizes the value of training for wearable vibrotactile devices. We discuss the implications of these findings for the design of tactile communication devices and wearable technology. Full article
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14 pages, 3919 KB  
Article
A Control Strategy for Mechatronic Action of a Pipe Organ Using a VCM Actuator
by Paweł Kowol, Paweł Nowak and Grazia Lo Sciuto
Electronics 2023, 12(23), 4754; https://doi.org/10.3390/electronics12234754 - 23 Nov 2023
Cited by 3 | Viewed by 2183
Abstract
In pipe organs, the oldest and most commonly chosen system for connecting the organist operator to the source of sound (i.e., the pipes to the action) is mechanical action. This article presents a mechatronic action with a voice coil motor (VCM) actuator to [...] Read more.
In pipe organs, the oldest and most commonly chosen system for connecting the organist operator to the source of sound (i.e., the pipes to the action) is mechanical action. This article presents a mechatronic action with a voice coil motor (VCM) actuator to reproduce the action of a mechanical action on pipe organ. The mechatronic action makes it feasible to mechanically separate the keyboard from the pipes and to determine the control strategy for the mechatronic action by utilizing sensors, an actuator and a microcontroller. The time response of the organ pipe with mechanical action and the requirements for mechatronic action were outlined. The control strategy was preceded by measurements of the mechanical action and measurements of the behavior of the VCM actuator system, which moves the pneumatic valve pallet. Two control strategies, open-loop and closed-loop, were proposed and analyzed for the mechatronic action with the VCM actuator. According to the results, the suggested control strategies successfully reproduce the mechanical action’s behavior to a good extent. Full article
(This article belongs to the Section Systems & Control Engineering)
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20 pages, 6159 KB  
Article
High-Performance Flux Tracking Controller for Reluctance Actuator
by Yang Liu, Qian Miao and Yue Dong
Appl. Sci. 2023, 13(19), 10811; https://doi.org/10.3390/app131910811 - 28 Sep 2023
Cited by 1 | Viewed by 1655
Abstract
To meet the ever-increasing demand for next-generation lithography machines, the actuator plays an important role in the achievement of high acceleration of the wafer stage. However, the voice coil motor, which is widely used in high-precision positioning systems, is reaching its physical limits. [...] Read more.
To meet the ever-increasing demand for next-generation lithography machines, the actuator plays an important role in the achievement of high acceleration of the wafer stage. However, the voice coil motor, which is widely used in high-precision positioning systems, is reaching its physical limits. To tackle this problem, a novel way to design the actuator using the magnetoresistance effect is argued due to the high force densities. However, the strong nonlinearity limits its application in the nan-positioning system. In particular, the hysteresis is coupled with eddy effects and displacement, which lead to a rate-dependent and displacement-dependent hysteresis effect in the reluctance actuator. In this paper, a Hammerstein structure is used to model the rate-dependent reluctance actuator. At the same time, the displacement-dependent of the model is regarded as the interference with the system. Additionally, a control strategy combining inverse model compensation and the disturbance observer-based discrete sliding mode control was proposed, which can effectively suppress the hysteresis effect. It is worthy pointing out that the nonlinear system is transformed into a linear system with inversion bias and disturbance by the inverse model compensation. What is more, the sliding mode controller based on the disturbance observer is designed to deal with the unmodeled dynamics, displacement disturbances, and model identification errors in linear systems. Thus, the tracking performance and robustness to external disturbances of the system are improved. The simulation results show that it is superior to the PI controller combined with an inverse compensator and even to the discrete sliding mode controller connected with inverse compensator, confirming the effectiveness of the novel control method in alleviating hysteresis. Full article
(This article belongs to the Special Issue New Technology for Autonomous UAV Monitoring)
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14 pages, 2156 KB  
Article
Effects of Stimulus Frequency and Location on Vibrotactile Discrimination Performance Using Voice Coil Actuators on the Forearm
by Nashmin Yeganeh, Ivan Makarov, Runar Unnthorsson and Árni Kristjánsson
Actuators 2023, 12(6), 224; https://doi.org/10.3390/act12060224 - 28 May 2023
Cited by 11 | Viewed by 5372
Abstract
What are the effects of frequency variation of vibrotactile stimuli on localization acuity? The precise localization of vibrotactile stimuli is crucial for applications that are aimed at conveying vibrotactile information. In order to evaluate the ability to distinguish between vibrotactile stimuli based on [...] Read more.
What are the effects of frequency variation of vibrotactile stimuli on localization acuity? The precise localization of vibrotactile stimuli is crucial for applications that are aimed at conveying vibrotactile information. In order to evaluate the ability to distinguish between vibrotactile stimuli based on their frequency and location on the forearm, we used a relative point localization method. Participants were presented with pairs of sequential vibrotactile stimuli at three possible locations on the forearm and asked to determine whether the second stimulation occurred at the same location as the first one in the pair or not. The stimulation frequency varied between 100 Hz, 150 Hz, 200 Hz and 250 Hz, which covers the range of frequencies that human observers are most sensitive to. The amplitude was kept constant. Our results revealed that the ability to discriminate between actuators remained unaffected by variations in the frequency of vibrotactile stimulation within the tested frequency range. The accuracy of the tactile discrimination task was heavily dependent on the location of the stimulation on the forearm, with the highest accuracy close to the wrist and elbow, locations that may serve as tactile anchor points. Our results highlight the critical role of stimulation location in precise vibrotactile localization and the importance of careful consideration of location in the design of forearm-mounted vibrotactile devices. Full article
(This article belongs to the Section Control Systems)
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16 pages, 8377 KB  
Article
Sixty-Nine-Element Voice Coil Deformable Mirror for Visible Light Communication
by Lv Jiang, Lifa Hu, Qili Hu, Xingyu Xu, Jingjing Wu, Lin Yu and Yang Huang
Photonics 2023, 10(3), 322; https://doi.org/10.3390/photonics10030322 - 17 Mar 2023
Cited by 3 | Viewed by 3006
Abstract
To overcome the atmospheric turbulence aberration, and improve the quality of light beam in visible light communication (VLC), a compact 69-element deformable mirror (DM) using micro voice coil actuators was designed based on systematic theoretical analysis. The structural parameters of the micro voice [...] Read more.
To overcome the atmospheric turbulence aberration, and improve the quality of light beam in visible light communication (VLC), a compact 69-element deformable mirror (DM) using micro voice coil actuators was designed based on systematic theoretical analysis. The structural parameters of the micro voice coil actuator were optimized by electromagnetic theory and the finite element method. The DM was optimized from the aspects of thermal deformation, response time, coupling coefficient, and other parameters. Finally, wavefront fitting and residual calculation were completed according to the influence function. The optimized voice coil deformable mirror (VCDM) has a large phase stroke, good thermal stability, a short response time of less than 0.7 ms, and a large first resonance of 2045 Hz. The fitting residuals of the VCDM for the first 10 Zernike modes with a PV value of 8 μm are all below 10 nm (RMS). Compared with a similar DM, the obtained results from our compact VCDM indicate that it has a higher wavefront fitting precision. VCDM corrected complex random aberrations in the VLC scenario and improved the coupling efficiency of the signal beam, proving that the compact VCDM with high performance and low cost has a good application prospect in VLC systems. Full article
(This article belongs to the Special Issue Visible Light Communications)
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19 pages, 5423 KB  
Article
Design and Implementation of an Active Vibration Control Algorithm Using Servo Actuator Control Installed in Series with a Spring-Damper
by Soo-Min Kim, Dae W. Kim and Moon K. Kwak
Appl. Sci. 2023, 13(5), 3349; https://doi.org/10.3390/app13053349 - 6 Mar 2023
Cited by 8 | Viewed by 10112
Abstract
The membrane-type air spring can be used to suppress lateral vibration of a vibration isolation table. However, compared to voice coil actuators, pneumatic actuators are difficult to use for precise vibration control, because servo valves have nonlinear dynamic characteristics. Therefore, actuators, such as [...] Read more.
The membrane-type air spring can be used to suppress lateral vibration of a vibration isolation table. However, compared to voice coil actuators, pneumatic actuators are difficult to use for precise vibration control, because servo valves have nonlinear dynamic characteristics. Therefore, actuators, such as voice coil actuators, can be placed in parallel with air springs, allowing force-type actuators to provide additional force to the system. These actuators generate force. In the case of a ball-screw mechanism device or a linear servomotor, it is an actuator that generates displacement. These actuators are represented as serial active systems. Serial active systems are structurally simpler than parallel active systems. However, there are very few studies on vibration isolation systems using serial active systems compared to parallel active systems. As the two are different types of systems, a new control algorithm suitable for the serial active system is needed. This study proposes a system in which an actuator capable of accurately controlling displacement is connected in series with a support spring-damper. A new active vibration control algorithm for the proposed control system is also developed, which is termed the position input and position output. The proposed control algorithm uses the displacement of the system as an input and outputs the desired displacement of the actuator installed in series with the damper and spring. The proposed control algorithm increases the damping at the target frequency and reduces the response of the system. Numerical studies and experiments were conducted on the single-degree-of-freedom and multi-degree-of-freedom systems. The results show the efficacy of the proposed control system and the novel control algorithm for the vibration suppression of the lateral vibration of a vibration isolation table. Full article
(This article belongs to the Special Issue Active Vibration and Noise Control)
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11 pages, 1942 KB  
Article
Evaluating the Optimum Distance between Voice Coil Actuators Using the Relative Point Localization Method on the Forearm
by Nashmin Yeganeh, Ivan Makarov, Snorri Steinn Stefánsson Thors, Árni Kristjánsson and Runar Unnthorsson
Actuators 2023, 12(1), 6; https://doi.org/10.3390/act12010006 - 22 Dec 2022
Cited by 7 | Viewed by 3274
Abstract
While vibrotactile stimulation shows promise for sensory substitution devices, a crucial question concerns vibrotactile spatial resolution. We examined the optimum distance between three voice coil actuators (model: lofeltL5) on the forearm. Three actuators were embedded in a fabric-based vibrotactile sleeve where the actuators [...] Read more.
While vibrotactile stimulation shows promise for sensory substitution devices, a crucial question concerns vibrotactile spatial resolution. We examined the optimum distance between three voice coil actuators (model: lofeltL5) on the forearm. Three actuators were embedded in a fabric-based vibrotactile sleeve where the actuators were placed in enclosures 3D-printed on the fabric. We used the relative point localization method where observers must discriminate whether two successive stimulations are in the same location or not. The resolution was measured for five vibrotactile sleeves, each with different distances between the actuators on the longitudinal axis of the forearm. The various distances were tested in a random order. In experiment one, pairs of stimuli were delivered sequentially in a random order to two adjacent actuators of the tactile sleeve on the upper side of the forearm. The task was to identify the perceived direction of the second stimulation (up, down, or the same) relative to the first one. Experiment two involved the same procedure but for the underside of the forearm. Taking the restrictions of the physical dimensions of the forearm and the design considerations into account, our results suggest that 20 mm is the optimum distance between the voice coil actuators (Model: Lofelt L5) for successful discrimination with high accuracy between the two stimulus locations on the forearm. There were no significant differences between the upper and undersides of the forearm. Full article
(This article belongs to the Section Actuator Materials)
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12 pages, 3406 KB  
Article
Active Disturbance Rejection Control of Voice Coil Motor Active Suspension Based on Displacement Feedback
by Feng Pan, Junlin Luo and Wei Wu
Actuators 2022, 11(12), 351; https://doi.org/10.3390/act11120351 - 29 Nov 2022
Cited by 8 | Viewed by 3754
Abstract
Electromagnetic active suspension is an important technique used in vehicles to improve ride comfort and handling stability. To achieve satisfactory suspension performance, the active suspension control requires strong robustness against the vehicle uncertainties and external disturbances. The voice coil motor (VCM) is applied [...] Read more.
Electromagnetic active suspension is an important technique used in vehicles to improve ride comfort and handling stability. To achieve satisfactory suspension performance, the active suspension control requires strong robustness against the vehicle uncertainties and external disturbances. The voice coil motor (VCM) is applied to the active suspension. A suspension model considering the actuator is established. An active suspension controller based on the active disturbance rejection control (ADRC) method is proposed. Through the test platform built, it is demonstrated that the ADRC of VCM active suspension has better performance than the PID. The results indicate that the overshoot and adjustment time of ADRC controller is reduced by 80% and 50%, respectively. The body vertical displacement of the ADRC is 50% smaller than PID. Full article
(This article belongs to the Section Control Systems)
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17 pages, 8671 KB  
Article
Three-Degree-of-Freedom Voice Coil Actuator Driven by a Four-Phase Current
by Akira Heya and Katsuhiro Hirata
Sensors 2022, 22(18), 6926; https://doi.org/10.3390/s22186926 - 13 Sep 2022
Cited by 4 | Viewed by 2756
Abstract
Camera attitude control systems for robots require a compact structure and high responsiveness. However, due to the combination structure of several actuators, the camera attitude control system is large. To address this issue, this study proposes a three-degree-of-freedom (3DOF) voice coil actuator. A [...] Read more.
Camera attitude control systems for robots require a compact structure and high responsiveness. However, due to the combination structure of several actuators, the camera attitude control system is large. To address this issue, this study proposes a three-degree-of-freedom (3DOF) voice coil actuator. A single actuator is used to generate 3DOF motion, which is driven by a four-phase current. This study also describes the basic structure and operating principle of the actuator and clarifies the torque characteristics using a three-dimensional (3D) finite element method (FEM). Furthermore, the dynamic modeling and control methods are presented. The FEM and dynamic simulation results reveal that the proposed actuator can be arbitrarily driven in 3DOF. Full article
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